So TAT is skin temp at the probes, which are rearward of the hottest skin according to that diagram. Was there a 'compensation' built into the TAT readout to account for the relatively rearward position of the TAT probes?
And.. How was static temp readout derived?
Er - no, the TAT probes measure just what they say Total
Air Temperature.
They are mounted off the skin and in freestream, so they measure the same temperature as would a probe on the nose.
Somewhere near the nose (not exactly on it, as the aircraft flies with a small AoA) there will be a 'stagnation' streamline where the oncoming air is brought to rest. At this point the skin temperature will be equal to the stagnation temperature (TAT). Behind that it gets more complicated! The skin temperature would depend on SAT, local Mach No, local skin friction coefficient (Mach and Re dependent, so varies with distance from nose), amount of heat radiated into space (paint colour!) and the amount of structure available to conduct heat away from the skin into the fuel (so roughly varying with thickness/chord and fuel distribution perhaps?
Static temperature and total temperature are related by a simple expression:
TAT = SAT *(1+0.2m^2) all in deg K
So in the troposphere at ISA +5 and Mach 2, SAT = 222 and TAT = 400.